Multi-Step Assessment of Lactation Curve Functions of Iranian Simmental and Jersey Cows with Emphasis on Relative Information Criteria
Subject Areas : CamelR. Pahlavan 1 , M.R. Afrazandeh 2 , N. Jamali 3 , M. Kazemi 4 , M.A. Abbasi 5 , J. Rahmaninia 6 , A. Kazemi 7 , B. Mohammad Nazari 8
1 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
2 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
3 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
4 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
5 - Department of Animal Science, Animal Science Research Institute of Iran (ASRI), Agricultural Research Education and Extension Organization (AREEO), Karaj, Iran
6 - Department of Animal Science, Animal Science Research Institute of Iran (ASRI), Agricultural Research Education and Extension Organization (AREEO), Karaj, Iran
7 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
8 - Animal Breeding Centre and Promotion of Animal Products, Ministry of Agriculture, Karaj, Iran
Keywords: milk production, dairy breed, empirical, mechanistic function,
Abstract :
Dairy herd improvement (DHI) programs and national genetic evaluation at the individual and/or herds levels rely on adjusted 305 d lactation performance predicted by lactation curve functions. These functions are approximations of real curves. To find the best function, multi-step assessment of predicted lactation curves is required. The purpose of this study was to investigate four-step examination of two-parameter Pollott mechanistic function and compare it with two empirical functions (Wood and Wilmink) to choose the one that best suited individual lactation curves in Jersey and Simmental cattle populations, independently. Wilmink had the lowest BIC for both breeds, while the Pollott had the lowest AICc value (although the difference with other functions is negligible) and produced the most typical curves, so could be the best fit. Moreover, the correlations between curve parameters in the Pollott function were the lowest for both breeds; demonstrating the independence of the evaluated parameters and the strength of that. In the best function (Pollott), the mean and annual trends for the estimated total lactation milk yield were 6082.1 kg and 48.01 kg for Simmental, and 6747.9 kg and 148.33 kg for Jersey cows, respectively. Overall, our results confirm that the Pollott's mechanistic function outperforms the other two functions for fitting individual lactation curves. It is more robust in terms of: (1) maximum number of standard curves, (2) lowest AICc, (3) independent curve parameters, and (4) biological interpretation of typical curves. Therefore, it could be recommended for practical implications of fitting and standardization of test-day yield of these two breeds.
Abbasi M., Pahlavan R., Afrazandeh M., KazemiM., HassaniBaferani A., Kazemi A. and Jamali N. (2021). Investigation of standard and atypical lactation curves of simmental and jersey cows in iran. Iranian J. Anim. Sci. 52, 123-131.
Albarran-Portillo B. and Pollot G.E. (2008). Genetic parametersderived from using a biological model of lactation on records of commercial dairy cows. J. Dairy Sci. 91, 3639-3648.
Albarrán-Portillo B. and Pollott G.E. (2013). The relationship between fertility and lactation characteristics in Holstein Cows on United Kingdom commercial dairy farms. J. Dairy Sci. 96, 635-646.
Anderson D.R. (2008). Model Based Inference in the Life Sciences: A Primer on Evidence. Springer, New York.
Angeles-Hernandez J.C., Pollott G.E., Albarran-Portillo B., Ramírez-Perez A.H., Lizarazo-Chaparro A., Ortega O.A.C. and Ronquillo M.G. (2018). The application of a mechanistic model to analyze the factors that affect the lactation curve parameters of dairy sheep in Mexico. Small. Rumin. Res. 164, 58-63.
Bang N.N., Gaughan J.B., Hayes B.J., Lyons R.E. and McNeill D.M. (2022). Application of infrared thermal technology to assess the level of heat stress and milk yield reduction of cows in tropical smallholder dairy farms. J. Dairy Sci. 105, 8454-8469.
Burnham K.P. and Anderson D.R. (2002). A Practical Information-Theoretic Approach. Model Selection and Multimodal Inference. Springer-Verlag, New York.
Burnham K.P., Anderson D.R. and Huyvaert K.P. (2011). AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons. Behav. Ecol. Sociobiol. 65, 23-35.
Cankaya S., Unalan A. and Soydan E. (2011). Selection of a mathematical model to describe the lactation curves of Jersey cattle. Arch. Anim. Breed. 54, 27-35.
Dematawewa C.M., Pearson R.E. and VanRaden P.M. (2007). Modeling extended lactations of Holsteins. J. Dairy Sci. 90, 3924-3936.
Dijkstra J., France J., Dhanoa M.S., Maas J.A., Hanigan M.D. and Beever A.J. (1997). A model to describe growth patterns of the mammary gland during pregnancy and lactation. J. Dairy Sci. 80, 2340-2354.
Dijkstra J., López S., Bannink A., Dhanoa M.S., Kebreab E., Odongo N.E., Nasri M.F., Behera U.K., Hernandez-Ferrer D. and Franc J. (2010). Evaluation of a mechanistic lactation model using cow, goat and sheep data. J. Agric. Sci. 148, 249-262.
Elzhov T.V., Mullen K.M., Spiess A.N., Bolker B., Mullen M.K.M. and Suggests M.A.S.S. (2016). Package ‘minpack. lm’. Title R Interface Levenberg-Marquardt Nonlinear Least-Sq. Algorithm Found MINPACK Plus Support Bounds.
Hebbali A. and Hebbali M.A. (2017). Package ‘olsrr’. Version 0.5, 3. Available at: https://olsrr. rsquaredacademy.com.
Hossein-Zadeh G.N. (2016). Modelling lactation curve for fat to protein ratio in Holstein cows. Anim. Sci. Pap. Rep. 34, 233-246.
Jeretina J., Babnik D. and Škorjanc D. (2013). Modeling lactation curve standards for test-day milk yield in Holstein, Brown Swiss and Simmental cows. J. Anim. Plant Sci. 23, 754-762.
Karamfilov S. and Nikolov V. (2019). First lactation milk production of cows of the Simmental breed reared in Bulgaria. Bulgarian J. Agric. Sci. 25, 363-369.
Knob D.A., Scholz A.M., Alessio D.R., Mendes B.P., Perazzoli L., Kappes R. and Neto A.T. (2019). Reproductive and productive performance, udder health, and conformation traits of purebred Holstein, F1, and R1 crossbred Holstein × Simmental cows. Trop. Anim. Health. Prod. 17, 1-9.
Kong L.N., Li J.B., Li R.L., Zhao X.X., Ma Y.B., Sun S.H., Huang J.M., Ju Z.H., Hou M.H. and Zhon F. (2018). Estimation of 305-day milk yield from test-day records of chinese Holstein cattle. J. Appl. Anim. Res. 46, 791-797.
Kopec T., Chládek G., Falta D., Kučera J., Večeřa M. and Hanuš O. (2021). The effect of extended lactation on parameters of Wood’s model of lactation curve in dairy Simmental cows. Anim. Biosci. 34, 949-957.
Kopec T., Chládek G., Kučera J., Falta D., Hanuš O. and Roubal P. (2013). The effect of the calving season on the Wood’s model parameters and characteristics of the lactation curve in Czech Fleckvieh cows. Arch. Anim. Breed. 56, 808-815.
Macciotta N.P.P., Vicario D. and Cappio-Borlino A. (2005). Detection of different shapes of lactation curve for milk yield in dairy cattle by Empirical Mathematical models. J. Dairy Sci. 88, 1178-1191.
Macciotta N.P.P., Dimauro C., Rassu S.P.G., Steri R. and Pulina G. (2011). The Mathematical description of lactation curves in dairy cattle. Italian J. Anim. Sci. 10, 51-63.
Mohanty B.S., Verma M.R., Sharma V.B. and Patil V.K. (2019). Effect of parity on the shape of lactation curves in purebred Jersey cows in Indian conditions. Biol. Rhythm Res. 53, 1-14.
Montgomery D.C., Peck E.A. and Vining G.G. (2021). Introduction to Linear Regression Analysis. John Wiley and Sons, New Jersey, United States.
Pollott G.E. (2000). A biological approach to lactation curve analysis for milk yield. J. Dairy Sci. 83, 2448-2458.
Rekaya R., Carabano M.J. and Toro M.A. (2000). Bayesian analysis of lactation curves of Holstein-Friesian cattle using a Nonlinear model. J. Dairy Sci. 83, 2691-2701.
Rook A.J., France J. and Dhanoa M.S. (1993). On the mathematical description of lactation curves. J. Agric. Sci. 121, 97-102.
SAS Institute. (2004). SAS®/STAT Software, Release 9.4. SAS Institute, Inc., Cary, NC. USA.
Silvestre A.M., Martins A.M., Santos V.A., Ginja M.M. and Colaço J.A. (2009). Lactation curves for milk, fat and protein in dairy cows: A full approach. Livest. Sci. 122, 308-313.
Tedeschi L.O. (2006). Assessment of the adequacy of mathematical models. Agric. Syst. 89, 225-247.
Torshizi M.E., Aslamenejad A.A., Nassiri M.R. and Farhangfar H. (2011). Comparison and evaluation of mathematical lactation curve Functions of Iranian Primiparous Holsteins. South African J. Anim. Sci. 41, 104-115.
Torshizi M.E. and Farhangfar H. (2020). The use of Dijkstra Mechanistic model for genetic analysis of the lactation curve characteristics and their relationships with age at first calving and somatic cell score of Iranian dairy cows. Acta Sci. Anim. Sci. 42, 1-12.
Wilmink J.B.M. (1987). Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation. Livest. Prod. Sci. 16, 335-348.
Wood P.D.P. (1967). Algebraic model of the lactation curve in cattle. Nature. 216, 164-165.